Quantum Diffusion and Eigenfunction Delocalization in a Random Band Matrix Model

We consider Hermitian and symmetric random band matrices H in d ≥ 1 dimensions. The matrix elements H xy , indexed by , are independent, uniformly distributed random variables if is less than the band width W , and zero otherwise. We prove that the time evolution of a quantum particle subject to the...

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Veröffentlicht in:Communications in mathematical physics Jg. 303; H. 2; S. 509 - 554
Hauptverfasser: Erdős, László, Knowles, Antti
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer-Verlag 01.04.2011
Springer
Schlagworte:
Algebra
Classical and Quantum Gravitation
Complex Systems
Exact sciences and technology
Linear and multilinear algebra, matrix theory
Mathematical and Computational Physics
Mathematical methods in physics
Mathematical Physics
Mathematics
Nonlinear algebraic and transcendental equations
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Other topics in mathematical methods in physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Sciences and techniques of general use
Theoretical
Quantum Diffusion
Heat Kernel
Chebyshev Polynomial
Anderson Model
Band Matrice
Band matrix
Symmetric matrix
Hamiltonians
Eigenfunctions
Eigenvectors
Localization
Random variable
Mathematical physics
ISSN:0010-3616, 1432-0916
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Beschreibung
Zusammenfassung:We consider Hermitian and symmetric random band matrices H in d ≥ 1 dimensions. The matrix elements H xy , indexed by , are independent, uniformly distributed random variables if is less than the band width W , and zero otherwise. We prove that the time evolution of a quantum particle subject to the Hamiltonian H is diffusive on time scales . We also show that the localization length of the eigenvectors of H is larger than a factor W d /6 times the band width. All results are uniform in the size of the matrix.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-011-1204-2